Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform.

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD - we have considerably increased algorithm's application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data.